Let V be a vector space. Prove that the zero vector and the
additive inverse are unique.

Answer:

10 cm is 20% of 50 cm.

Step-by-step explanation:

1) Put the "question" into fraction form: 10/50

2) Divide the numerator by the denominator (essentially changing the fraction into the decimal form): 10 ÷ 50 = 0.2

3) Multiply the quotient by 100: 0.2 × 100 = 20

4) Slap a "%" on the end and you're good to go!! : 20%

The width of the photograph is approximately 10.5 inches.

Let's first write an expression for the length of the photograph in terms of its width

Length = Width + 6 inches

And we know that the area of the photograph is given by

Area = Length × Width

Substituting the expression for the length, we get

Area = (Width + 6) × Width

Simplifying this expression, we get

Area = Width^2 + 6 Width

We are given that the area of the photograph is 132 square inches. So we can set up an equation

132 = Width^2 + 6 Width

Rearranging this equation, we get a quadratic equation in standard form

Width^2 + 6 Width - 132 = 0

Now we can solve for the width using the quadratic formula

Width = (-6 ± √(6^2 - 4(1)(-132))) / (2(1))

Width = (-6 ± √(1416)) / 2

We can simplify this expression

Width = (-3 ± √354)

Since the width must be positive, we can discard the negative solution

Width = (-3 + √354) ≈ 10.5 inches

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The F-test statistic is approximately 0.9258.

To find the F-test statistic to test the claim that the variances of the two populations are equal, we can use the formula:

F = (s₁² / s₂²), where s₁² is the variance of the first sample and s₂² is the variance of the second sample.

In this case, the standard deviation of the first sample is 11.6185, which means the variance is (11.6185)² = 135.0555. The standard deviation of the second sample is 12.0756, so the variance is (12.0756)² = 145.8939.

F = (135.0555 / 145.8939)

F ≈ 0.9258

Therefore, the F-test statistic to test the claim that the variances of the two populations are equal is approximately 0.9258.

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Answer:

Sara's number is 28

Step-by-step explanation:

Let's assign Sara's number the variable x and solve this equation using the information provided.

"If you subtract 14 from my number"

x - 14

"and multiply the difference by - 3"

-3(x - 14)

"the result is – 42."

-3(x - 14) = -42

Now we can solve from here for x.

-3(x - 14) = -42

x - 14 = 14

x = 28

Answer:

12x-8 ______

Step-by-step explanation:

The second bit, I have no clue. But the first is just simplifying in algebra.

Answer: E. All hemlock trees in the forest from which the 200 trees were selected

Step-by-step explanation:

When we generalize data, it needs to be about a sample that is as specific as possible so that the generalization has a better chance of holding true.

The best group of trees to generalize the data on is the trees in the forest where the hemlock trees were found. This is a specific population and has a higher chance of being right because the trees used in research could not have been the only ones suffering.

If we use a × b, then it means that a is b times more than a and if we use a/b it means that we are making parts of a by the factors of b.

A mathematical expression that specifies the objects to be multiplied, known as a factor, produces a product. The other operations are multiplication, addition, and subtraction. When two natural numbers are divided with a remainder, or in the Euclidean method, the result is an integer quotient, which is the number of times the second number is entirely contained in the first number, and a remainder, which is the portion of the first number that remains after computing the quotient.

Rule of Division and Multiplication of Integers

Multiplication:

Rule 1: A positive integer and a negative integer cannot be added together.

Rule 2: A positive number is the result of two positive integers.

Rule 3: It states that the sum of two negative integers is positive.

Examples:

Rule 1: 1. (+4) x (-2) = -8 2. (-2) x (+5) = -10

Rule 2: 1. (+6) x (+8) = +48 2. (+6) x (+2) = +12

Rule 3: 1. (-6) x (-8) Equals +48 2. (-2) x (-4) = +8

Division:

Rule 1: A positive integer and a negative integer cannot be multiplied together.

Rule 2: A positive number is the quotient of two positive integers.

Rule 3: A positive number is the quotient of two negative integers.

Examples:

Rule 1: 1. (-8) / (+4) = -2 2. (-12) / (+6) = -2

Rule 2: 1. (+6) / (-3) = -2 2. (+24) / (-6) = -4

Rule 3. 1. (+9) / (+3) = +3 2. (+16) / (+4) = +4

Rule 4: 1. (-6) / (-2) = +3 2. (-42) / (-7) = +6

This is the summary of multiplication and division rules.

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Answer:

value of x is for values that are excludedor or left out

Answer:

She spends 36 minutes doing backstroke.

Step-by-step explanation:

\(0.4\) × \(90 = 36\)

Answer:

2,1

Step-by-step explanation:

The yield to maturity of a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons, if the =bond is currently trading for a price of $884, is 6.23%. Thus, option a and option b is correct

Yield to maturity (YTM) is the anticipated overall return on a bond if it is held until maturity, considering all interest payments. To calculate YTM, you need to know the bond's price, coupon rate, face value, and the number of years until maturity.

The formula for calculating YTM is as follows:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

Where:

C = Interest payment

F = Face value

P = Market price

n = Number of coupon payments

Given that the bond has a coupon rate of 5.2%, a face value of $1000, a maturity of ten years, semi-annual coupon payments, and is currently trading at a price of $884, we can calculate the yield to maturity.

First, let's calculate the semi-annual coupon payment:

Semi-annual coupon rate = 5.2% / 2 = 2.6%

Face value = $1000

Market price = $884

Number of years remaining until maturity = 10 years

Number of semi-annual coupon payments = 2 x 10 = 20

Semi-annual coupon payment = Semi-annual coupon rate x Face value

Semi-annual coupon payment = 2.6% x $1000 = $26

Now, we can calculate the yield to maturity using the formula:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

YTM = (2 x $26 + ($1000-$884)/20) / (($1000+$884)/2) x 100

YTM = 6.23%

Therefore, If a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons is now selling at $884, the yield to maturity is 6.23%.

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Answer: Not sure if the second one is times or just the variable x, i assume its the variable x. Answer:

x=5

Step-by-step explanation:

Let's solve your equation step-by-step.

3x−12=−4x+23

Step 1: Add 4x to both sides.

3x−12+4x=−4x+23+4x

7x−12=23

Step 2: Add 12 to both sides.

7x−12+12=23+12

7x=35

Step 3: Divide both sides by 7.

7x

7

=

35

7

x=5

Answer:

x=5

Answer:

0.0863

Step-by-step explanation:

Given that:

The mean =145

The standard deviation = 11

To find P(X ≥ 160) :

Z = (x - μ)/σ

Z = 160 - 145/ 11

Z = 1.364

From the standard normal z table

Thus;

P(X ≥ 160) =  1- P(Z < 1.364)

P(X ≥ 160) = 1 - 0.9137

P(X ≥ 160) = 0.0863

\(5x+10y=25\)

Add -10y to both sides:

\(5x+10y+-10y=25+-10y\)

\(5x=-10y+25\)

Divide both sides by 5:

\(\dfrac{5x}{5} =\dfrac{-10y+25}{5}\)

\(\fbox{y = -2y + 5}\)

The explicit formula for f^-1 is (x-3)^(1/4) and this is obtained by switching the roles of x and y and solving for y in terms of x.

To find the inverse function of f(x)=x^4+3, we need to switch the roles of x and y, and solve for y.
Let y = x^4+3
Subtract 3 from both sides to get:
y - 3 = x^4
Take the fourth root of both sides to isolate x:
(x^4)^(1/4) = (y-3)^(1/4)
Simplify:
x = (y-3)^(1/4)
So the inverse function of f(x) is:
f^-1 (x) = (x-3)^(1/4)
This is the explicit formula for the inverse function of f(x).
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Answer:

18 feet

Step-by-step explanation:

The number of sides in a polygon is 9.

Given, a regular polygon is drawn in a circle so that each vertex is on the circle and is connected to the center by a radius and each of the central angles has a measure of 40°.We know that the sum of all the central angles of a polygon is 360°, so we can find the number of sides of a polygon as follows:Let the number of sides of a polygon be n.Measure of each central angle = 40°Sum of all the central angles = n × 40° = 360°So, n × 40° = 360°n = 360°/40°n = 9So, the polygon has 9 sides (nonagon).

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Answer:

The independent variable is the variable that is manipulated or changed during an experiment. In this case, the independent variable is represented by the x-values of the given points.

So, the answer would be option A: {-2, 3, 1, 5}

Step-by-step explanation:

brainliest Plsssss

The ordered points that are in the distance of 4.5 units is (5.5, -1) (-1.5, 3)

Ordered pair:

Ordered pairs is known as the pair of elements that occur in particular order.

Given,

Here we have the following points:

(5.5, -1) (-1, 3) (-3, 3) (5.5, 2.5) (-1.5, -1.5)

Now, we have to calculated the ordered pair whose point is 4.5 units apart.

In order to find the distance, we have to take the x axis value and then we have to find the difference between them.

Now, we have to take the points (5.5, -1) and (-1, 3)

The difference between these points is

=> 5.5 - 1.5

=> 4.5

Therefore, the resulting ordered pair is  (5.5, -1) and (-1, 3).

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Answer:

The answer is y=7.5x and y=5.5x+10

Answer:

How did you manage to get it upside down? impressive

Step-by-step explanation:

The answer is C because the slower slope value had +10 as the y intercept also you can clearly see the orange one is going at a faster rate

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\( \huge \rm\frac{x} {4} + \frac{x}{4} \\ \\ \huge \rm\frac{x + x}{4} \\ \\ \huge \rm \frac{2x}{4} \\ \\ \huge \blue{ \boxed{ \pink{ \rm \: \frac{x}{2} \: }}}\)

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I hope you understood!✏

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Answer:

We can use the Pythagorean theorem to find the length of the hypotenuse:

c^2 = a^2 + b^2

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

Plugging in the given values, we get:

c^2 = 16^2 + 10^2

c^2 = 256 + 100

c^2 = 356

Taking the square root of both sides, we get:

c = sqrt(356)

c ≈ 18.9

Therefore, the length of the hypotenuse is approximately 18.9 cm.

Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires.

Compound interest simply means that the interest associated with a bank account, loan, or investment increases exponentially over time.

Given monthly income of Ron is $3,142.23

Ron is 25 years old and is retiring at the age of 65. so he has 40 years to contribute.

Total amount he contribute in 40 years paying 5.5% compounded monthly is given by

interest rate(r) = 0.055/12

time period = 40 years = 480 months

Principal amount = $314.223

Future value = \(P(\frac{(1+r)^{n}-1 }{r} )\)

Substitute, we get,

= 3142.23 \(.10(\frac{(1+\frac{0.055)^{12.40}-1) }{12} }{\frac{0.055}{12} }\)

Thus, future value is $547074.681009.

After retirement his monthly income when he has $547074.681009 amount.

P = (A.i/2)/(1-(1+i/12)⁻ⁿ)

Putting values, we get,

P = (547074.68×0.55/12)/1-(1+0.055/12)⁻²⁴⁰

P = $3763.25

He will receive a monthly income of $3763.25.

But  given he will need a monthly income of $4,123 for 20 years, which is not met by Ron.

So, the amount he needs to supplement his monthly income when he retires by (4123-3763.25)= $359.74

Hence, Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires.

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When the L shape attached is rotated about the origin (0, 0) by 90° counterclockwise it would look like option C.

A shows a rotation of 90°  clockwise about (0,0)

B shows a rotation of 180° about (0,0)

C shows a rotation of 90° anticlockwise about (0,0)

D shows a rotation of 90° anticlockwise, but the center of rotation is (1,1)

Recall that Rotation in math is a transformation that involves rotating a figure around a fixed point called the center of rotation by a certain angle in a clockwise or counterclockwise direction.

Thus, Option C above is the right answer.

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Answer:   A

Step-by-step explanation:

Answer:

Subtraction

Step-by-step explanation:

To get x by itself, subtract 4 from both sides.

The value of variable x is given by the equation x = 7

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

x + 4 = 11

Subtracting 4 on both sides , we get

x = 11 - 4

On simplifying the equation , we get

x = 7

Therefore , the value of x is 7

Hence , the equation is x = 7

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The wavelength of the given speed and frequency would be = 0.062m

Speed is defined as the distance a wave travels in a given amount of time, such that it is measured in meters per second.

The frequency of a wave is defined as the number of cycles that can be completed in a given time. This is measured in Hertz (Hz).

The wavelength is defined as the distance if a wave which can be measured in meters.

The formula for wave speed = v = fλ

Where v = Speed = 5.410x10⁴

f = 872khz = 872000hz

λ = ?

make λ the subject of formula;

λ = 5.410x10⁴/872000

λ = 54100/872000

λ = 0.062m

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For the options C, D, and E, (where the 3 sides are given) result in the construction of unique triangles.

We will have unique triangles only if the length of the 3 sides are completely determined, so we need to know the 3 sides, or two sides and one angle.

With that in mind, for options C, D, and E (in the 3 cases the 3 sides of the triangles are given). Then for these 3 options, we can make a unique triangle.

While for the first two options, where we only know the angles, we can make infinite triangles.

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